A severe weather warning of heavy rain has been issued by the Met Office for Wales, the West Midlands and south-west England. Photograph: Christopher Thomond for the Guardian

Flooding could hit parts of the UK over the coming days as heavy rain sweeps across the country, forecasters say.

South-west England and Wales experienced deluges of 15-20mm overnight, with the wet weather expected to spread further east on Friday morning before clearing.

Further downpours were expected later on Friday and rainfall could reach 30mm by Saturday, according to experts.

A severe weather warning of heavy rain has been issued by the Met Office for Wales, the west Midlands and south-west England.

Issuing the yellow warning, which urges people to be prepared, the forecaster said: "Periods of heavy rain are likely across the southern half of Wales, south-west England and the south-west Midlands from the beginning of Friday until Saturday morning.

"It is looking increasingly likely that one area of heavy rain will move through during the small hours of Friday followed by a drier interlude, before further heavy, persistent rain moves eastwards later on Friday into the early hours of Saturday.

"However, there still remains considerable uncertainty in the details of the heavy rain by late Friday and the warning may be adjusted further as the event approaches.

"The public should be aware of the possibility of disruption to travel due to localised flooding."

Nick Prebble, a forecaster for MeteoGroup, the weather division of the Press Association, said 30mm of rain could hit areas of southern England and Wales: "It's going to be a wet one.".

The Environment Agency has 18 flood alerts in place in the south-west, Midlands, Anglian and north-east regions. Three flood warnings are in place in the north-east.

Met Office forecaster Greg Dewhurst said southern areas could expect temperatures of 14-15C (57-59F) over the next few days, with the London area reaching 17C.

Despite seeing spells of dry and sunny weather, northern areas will feel slightly cooler with temperatures between 12-14C, he said.